Abstract
Let BPL and BH denote the classifying spaces for stable PL block bundles [9] and stable homology cobordism bundles ([4], [5]). There is a natural map) : BPL -> BH with homotopy fibre denoted by H/PL._ If M is a closed (integral) homology manifold, a resolution of M is a pair (P,f), where P is a piecewise linear (PL) manifold a n d / : P -> M is a surjective PL map which is acyclic, i.e. ff*(f~(x)) = 0 for all x e M. Let T : M -» BH classify the homology tangent bundle of M. We prove the following theorems.
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